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Improved componentwise verified error bounds for least squares problems and underdetermined linear systems.
- Source :
-
Numerical Algorithms . Jun2014, Vol. 66 Issue 2, p309-322. 14p. - Publication Year :
- 2014
-
Abstract
- Recently Miyajima presented algorithms to compute componentwise verified error bounds for the solution of full-rank least squares problems and underdetermined linear systems. In this paper we derive simpler and improved componentwise error bounds which are based on equalities for the error of a given approximate solution. Equalities are not improvable, and the expressions are formulated in a way that direct evaluation yields componentwise and rigorous estimates of good quality. The computed bounds are correct in a mathematical sense covering all sources of errors, in particular rounding errors. Numerical results show a gain in accuracy compared to previous results. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 10171398
- Volume :
- 66
- Issue :
- 2
- Database :
- Academic Search Index
- Journal :
- Numerical Algorithms
- Publication Type :
- Academic Journal
- Accession number :
- 96330322
- Full Text :
- https://doi.org/10.1007/s11075-013-9735-6